Course Description

This is a one semester course in linear algebra with computer applications. We will be covering the following topics: matrices and matrix properties, vectors and vector spaces, linear systems, and linear transformations. The class lectures will focus primarily on definitions and theory, with some simple calculations being performed without the aid of a computer. After learning the basic principles and theory of each topic, we will reinforce the material using the open source mathematics software SAGE. Through a series of lab experiments, you will also gain familiarity with the programming language Python. Many of these lab experiments will focus on applications of linear algebra to other areas of mathematics and other fields, including data science.

Objectives

describe the solution(s) of a system of linear equations, or be able to decide that one does not exist.

be able to perform arithmetic operations on vectors and matrices, where defined.

calculate the determinant of a matrix, and understand its significance.

define a vector space and determine whether a set is a vector space.

find the basis and dimension of a vector space.

define and describe the four fundamental subspaces.

define and identify linear maps.

define and compute eigenvalues and eigenvectors.

explain the geometric effect of a linear transformation on 2-dimensional spaces.

produce and utilize simple Sage programs to perform computations related to all of the above topics.

Required Materials

Linear Algebra and its Applications, by David Lay, Steven Lay, and Judi McDonald, 5th Edition. No other supplies are required for the course. You will not need to purchase any software, access codes, or supplementary material with the text. Older editions may be used, but are discouraged (the fourth and fifth editions are quite different). A rental or electronic version is fine - you will not need to bring your book to class.

Textbook Homework

Suggested problems from the textbook for each section we will cover appear in the table below. Your work will not be collected. However, actually working through these problems is the key to your success in this class. Attending every class is not enough; mathematics can only be learned through practice. It is expected that you spend approximately 8-12 hours per week studying the material outside our class meetings, according to the typical 2-3 hours per credit rule.

Most of the problems will have solutions in the back of the textbook. Make sure to check your work. The exams will be based primarily on these problems.

Stay up to date with homework, and get help if you cannot understand a problem after trying it on your own. Do not ignore a problem that you are struggling with. If you are having trouble with a topic, please come talk to me during office hours, ask questions in class, or seek help from a classmate. You are expected to try to work on all problems on your own first; when coming to my office, be prepared to show me what you've already tried.

Section

Problems

1.1

1, 3, 5, 7, 9, 11, 13, 17, 19, 26

1.2

1, 3, 5, 7, 11, 17, 19, 29

1.3

1, 3, 5, 9, 11, 13, 15, 19, 21

1.4

1, 2, 3, 4, 5, 9, 11, 13, 15, 25, 29

1.5

1, 3, 5, 7, 11, 29, 31, 35

1.7

1, 3, 5, 7, 9, 15, 17, 19, 21, 25, 29

2.1

1, 2, 3, 7, 9, 10, 11, 15, 17, 27

2.2

1, 2, 3, 4, 7, 18, 29, 31, 32

2.3

1, 3, 5, 11, 13, 15

2.4

1, 3, 5, 7, 13

3.1

1, 3, 5, 9, 11, 21, 23, 37, 41

3.2

15, 17, 19, 21, 25, 29, 33, 35, 37, 39

3.3

1, 3, 5, 7, 19, 21, 23

4.1

1, 3, 5, 6, 7, 8, 9, 10, 11, 13, 21

4.2

1, 3, 5, 7, 9, 11

4.3

1, 3, 5, 7, 9, 15

4.5

1, 3, 5, 7, 9, 11, 13, 25

4.7

7, 9

5.1

1, 3, 5, 7, 9, 11, 13, 17, 19

5.2

1, 3, 5, 7, 9, 13, 15

5.3

1, 7, 9, 11

6.1

1, 3, 5, 7, 9, 11, 15, 17, 23, 25, 27

1.8

1, 3, 5, 9, 17, 33

1.9

1, 3, 5, 15, 17, 19, 21, 37

Quizzes

You will be given quizzes on the material regularly. Keeping up with the suggested textbook homework will ensure that you are prepared for the quizzes, which will feature problems very similar to those in the homework. The dates for quizzes is provided in the schedule below; note that exact topics covered on a quiz is subject to change. Any changes will be announced in class.

Quiz grades will not be based strictly on whether or not you found the correct answer. Your work must also be written clearly, and with proper notation, to receive full credit.

Make up quizzes will only be given for excused absences. All make ups must be completed before the graded quizzes are returned to the class; this will typically be the next class meeting.

Exams

We will have two midterm exams. Use of notes, textbooks, calculators, electronic devices, or other materials will not be permitted during an exam. If you will not be able to attend class for a scheduled exam, please let me know before the exam is scheduled. Make up exams will be given for excused absences only.
Note that the exams are scheduled during our lab period. This will allow you more time to work on the exam.

Midterm 1: Thursday, September 28

Midterm 2: Thursday, November 2

The final exam will be cumulative, and is scheduled for Friday, December 15, 10:30 - 12:30.

Final Grades

Your final grade will be calculated as follows:

Midterm Exams: 40%

Final Exam: 20%

Quizzes: 20% (lowest quiz grade is dropped)

Labs: 20% (lowest lab grade is dropped)

Your letter grade will be determined according to the department grading scale:

F

D

D+

C

C+

B

B+

A

0-59

60-66

67-69

70-76

77-79

80-86

87-89

90-100

Course Policies and Suggestions

On successful completion of the course, students should be able to:

If you are struggling with a topic, please come to office hours as soon as possible. Tutoring for this course can not be expected through our usual department tutors, but it may be possible to arrange private assistance. Don't let yourself fall behind!

Attendance is not required, but is highly recommended. If you have to miss class, read the relevant section of the textbook and try the suggested problems, and ask a classmate for notes and information you may have missed. I do not keep detailed lecture notes for this course.

I will attempt to return emails as quickly as possible (within 24 hours). However, it is better to ask complicated questions during class or in office hours. If you have a question about the homework, it is quite likely someone else has the same question, so you’re doing the class a favor by asking.

There are other linear algebra textbooks available in the library and in my office. Due to book prices, you may not want to invest in a second book, but it can be helpful to have alternate sources or see topics explained in other ways. There are two recommended textbooks available free online:

I do not have a "no electronics" policy, and I'd prefer not to implement one. Please try to remember to mute all devices during lecture, and use devices in a way that does not distract other students in the class.

You will not need a calculator for this course, nor will you be permitted to use one on exams.

You will be allowed to listen to music (with headphones) during exams, but please keep the volume at a level that does not distract other students. Plan a playlist in advance - your phone/player will need to be kept face down on the desk throughout the exam.

Learning Differences

In keeping with college policy, any student with a disability who needs academic accommodations must call Learning Differences Program secretary at 824-3017, to arrange a confidential appointment with the director of the Learning Differences Program during the first week of classes.

Mercy Mission

This course supports the mission of Mercyhurst University by creating students who are intellectually creative. Students will foster this creativity by: applying critical thinking and qualitative reasoning techniques to new disciplines; developing, analyzing, and synthesizing scientific ideas; and engaging in innovative problem solving strategies.

Schedule

The exact topic covered on a particular date is subject to change. Exams and quizzes will be given on the day they are scheduled, though the sections appearing on a quiz may differ. Announcements will be made in class regarding any schedule changes.